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If you weighed a mirror in a room with no light, and then weighed a mirror in a well lit room so that the mirror reflects light, would the weight be different?

Jim
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Brent
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    No. Why would it? – ACuriousMind May 18 '15 at 21:36
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    Momentum transfer –  May 18 '15 at 21:38
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    Why do you need the mirror? Just have a scale balanced at zero in perfect darkness, then turn on the light. Does the scale now measure any weight? – CJ Dennis May 19 '15 at 03:28
  • Most of the effect of the light on the mirror will be on the non-reflective side, such as heating it up. – dotancohen May 19 '15 at 07:43
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    Yes. In fact, this is how solar sails work. – Yves Klett May 19 '15 at 09:05
  • @Brent Do you perhaps mean to ask if its mass increases? Weight is relative to the device measuring it. – thanby May 19 '15 at 14:57
  • I think the title of this question is a bit misleading. This doesn't actually ask if a mirror image has a weight, it asks if a mirror itself weighs more with light reflecting off of it. I've gone ahead and modified it. Let me know if it conflicts with your intentions – Jim May 19 '15 at 15:21
  • Correct me if I am wrong but aren't photons supposed to be massless particles? – Karan Singh May 19 '15 at 16:45
  • @KaranSingh They are, but they have a momentum. So if you change that momentum by, say, reflecting them, you incur a reaction force, which can accelerate a mass. – Jim May 19 '15 at 17:04

5 Answers5

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Yes, if the mirror was on the floor and facing upward. The transfer of momentum as photons recoil from it and are absorbed by the surroundings would make it heavier.

dylan
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    Well, it would make the scales say it weighs more (if you had scales precise enough) at least. – Luaan May 19 '15 at 08:57
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    Yes that's more just pressure than actual weight. I think the question should be something more like "Does it increase the mirror's mass?" – thanby May 19 '15 at 14:54
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    This would only be the case if the photon pressure had a net downwards component. But if the mirror were oriented, for example, upright, you wouldn't have any change in measured weight. I know you covered this, I'm just adding a NB – Jim May 19 '15 at 15:45
  • @JimtheEnchanter most lights are on the ceiling, pointing down – AncientSwordRage May 19 '15 at 15:51
  • @Pureferret most mirrors are on the wall, pointing to the side. Clearly, we aren't working with the usual situations, but if we were, the location of the light source would be mostly irrelevant – Jim May 19 '15 at 15:57
  • Agree with Luaan and thanby - the photon pressure might add to the measured weight, but the true weight of the object is unchanged. Surely you wouldn't say the weight of the mirror increased if I were to rest my hand on the top of the mirror as you weighed it? :) – Kevin K May 19 '15 at 16:04
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    Yes, the mass of the mirror does not change but it weighs more –  May 19 '15 at 17:52
  • How much heavier? Estimated order of magnitude? – Anubian Noob May 19 '15 at 18:56
  • @DirkBruere ah, your statement confused me because I forget that there are multiple definitions of weight. I always treat 'weight' on its own to mean gravitational weight, not operational/apparent weight – Kevin K May 19 '15 at 23:22
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What about heating up the mirror? I assume not all light is reflected but also absorbed. Energy is related to mass.

Here is a summary of real experiments that show how kinetic energy in an object contributes to its gravitational mass:

arxiv:gr-qc/9909014

rob
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magforce
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    Well, it's probably not measurable since it will probably in the ng range, but the question was not about the order of magnitude! – magforce May 18 '15 at 23:42
  • Come to think of it, would the light actually transfer any heat to the mirror? Shouldn't it theoretically reflect all the light and therefore not absorb any as heat? – thanby May 27 '15 at 12:47
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Photons are elementary particles and they do have an invariant mass, when there are more than one of them: the addition of their four vectors. Example: pi0 into two gamma, those two gammas have the invariant mass of the pio0.

A dark mirror in principle should show a smaller mass because the photons which hit and reflect , at the time of hitting have an invariant mass which is overlaid on the mass of the mirror.

This is separate from momentum conservation showing up on a weight scale, radiation pressure. And separate from the absorption increase of mass .

Selene Routley
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anna v
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  • Hi Anna excellent point: you might like to link to https://www.fourmilab.ch/etexts/einstein/E_mc2/e_mc2.pdf which essentially is the same idea, although not expressed in as modern terms as yours. – Selene Routley May 19 '15 at 03:51
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Where is the light source? If the light source is above the midpoint of the mirror the mirror will weigh slightly more. However, if the light it below the mirror it's weight is going to drop. (This effect goes away if the mirror is absolutely perfect. Real world mirrors will absorb some photons, though.)

There will be a considerably stronger (but still infinitesimal) sideways force imposed on the mirror by the light bouncing off it. Even if the room is evenly lit this still pushes on the shiny side vs the non-reflecting back side.

Note that both of these factors apply relative to the mirror's orientation. Dirk Bruere's answer is force #2 applied to a mirror laying down.

Loren Pechtel
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While some light energy may be absorbed by the mirror, the only light that has an effect on the image is the light that bounces back off.

For the same reason a ball touching a bat isn't considered as an increase in bat weight, the mirror's weight is not considered as an increase when the light hits the glass.

Further, the light photons that are absorbed (and are not affecting the image appearance) affect nearly every object in similar ways. Thus it is not special to the image either.

Martin
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user3344751
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